Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

Abstract

The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the π 0 − γ * − γ * transition form factor based on the large-N C and short-distance properties of QCD. The resulting twoloop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining twodimensional integration over the moduli of the Euclidean loop momenta. The value obtained, a LbyL;π 0 µ = +5.8 (1.0) × 10 −10 , disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads a LbyL;π 0 µ | V M D = +5.6 × 10 −10 , and differs only by its overall sign from the value obtained by previous authors. The inclusion of the η and η ′ poles gives a total value a LbyL;PS µ = +8.3 (1.2) × 10 −10 for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of a µ and its theoretical counterpart in the standard model.

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